We prove that (additive) ordered group reducts of nonstandard models of the bounded arithmetical theory $\mathsf{VTC^0}$ are recursively saturated in a rich language with predicates expressing the integers, rationals, and logarithmically bounded numbers. Combined with our previous results on the construction of the real exponential function on completions of models of $\mathsf{VTC^0}$, we show that every countable model of $\mathsf{VTC^0}$ is an exponential integer part of a real-closed exponential field.

翻译：我们证明了有界算术理论$\mathsf{VTC^0}$的非标准模型的（加法）有序群归约在含有表示整数、有理数和对数有界数的谓词的丰富语言中是递归饱和的。结合我们先前关于在$\mathsf{VTC^0}$模型的完备化上构造实指数函数的结果，我们证明了$\mathsf{VTC^0}$的每个可数模型都是实闭指数域的指数整数部分。